How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?

Answers

Answer 1

120, 60
First answer is 5!, second answer is 5!/2 because swapping two z's does not generate a new permutation.

Answer 2

Case 1: If the letter z is distinctly different

If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = 120 different arrangements

Case 2: If the letter Z is interchangeable

If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2

So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = 60 arrangements

Related Questions

Sandy releases a javelin 1.6 m above the ground with an initial vertical velocity of 25 m/s. How long will it take the javelin to hit the ground?

Answers

Time taken for the javelin to hit the ground will be given by:
A(t)=V'(t)=S''(t)
A(t)=-9.8m/s
⇒V(t)=-9.8t/1+C m/s

Where C is the initial velocity:
⇒V(t)=-9.8t+25
⇒S(t)=-9.8t²/2+25t/1+C
⇒S(t)=-4.9t²+25t+C
but the C is the initial vertical displacement, hence:
S(t)=-4.9t²+25t+1.6m

The time taken to hit the ground will therefore be:
S(t)=0
-4.9t²+25t+1.6=0

Using a quadratic function, it is found that it will take 5.17 seconds for the javelin to hit the ground.

What is the quadratic function for a projectile's height?

Considering meters as the measure of height, it is given by:

h(t) = -4.9t² + v(0)t + h(0).

In which:

v(0) is the initial velocity.h(0) is the initial height.

In this problem, we have that v(0) = 25, h(0) = 1.6, hence:

h(t) = -4.9t² + 25t + 1.6

It hits the ground when h(t) = 0, hence:

-4.9t² + 25t + 1.6 = 0

4.9t² - 25t - 1.6 = 0.

Which is a quadratic function with coefficients a = 4.9, b = -25, c = -1.6. Hence:

[tex]\Delta = (-25)^2 - 4(4.9)(-1.6) = 656.36[/tex]

[tex]x_1 = \frac{25 + \sqrt{656.36}}{9.8} = 5.17[/tex]

[tex]x_2 = \frac{25 - \sqrt{656.36}}{9.8} = -0.06[/tex]

For time we want the positive value, hence, it will take 5.17 seconds for the javelin to hit the ground.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ2

Kali invests $3516 in a savings account with a fixed annual interest rate of 7% compounded 3 times per year. What will the account balance be after 7 years

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$3516\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{well, is just three} \end{array}\to &3\\ t=years\to &7 \end{cases} \\\\\\ A=3516\left(1+\frac{0.07}{3}\right)^{3\cdot 7}\implies A=3516\left( \frac{307}{300} \right)^{21}\implies A\approx 5707.0070[/tex]

please help no will mark brainlyst

Explain how you would find 90% of 120.

Answers

Our trick here is to think that a fraction in %

land is the same as the correspondent in "number" land; so we can write:
100%
90%
= 120x
Where X is the correspondent of 90% in numbers.
Rearranging: x = 120⋅
90% 100% =108

If 120 = 100% then how much of it is 90%?

To find out you will have to multiply 90 with 120 and then divide what you get with 100.

90 x 120 = 10800

10800/100 = 108

so 90% of 120 is 108.

Hope this helped :)

Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16

pppppppllllllleeeeaaaassssseeeee ANSWER FASRT

Answers

no. of real solns depends on the term b^2 - 4ac for y = ax^2 + bx + c
if its <0, no real soln
its =0, 1 real soln
its >0, 2 real solns

for
y = -3x2 + x + 12, 1^2-4(-3)(12) > 0, two solns
y = 2x2 - 6x + 5, -6^2-4(2)(5) < 0, no soln
y = x2 + 7x - 11, 7^2-4(1)(-11) > 0, two solns
y = -x2 - 8x - 16, -8^2-4(-1)(-16) = 0, one soln

According to the discriminant:

[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.

The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].

If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.

Equation [tex]y = -3x^2 + x + 12[/tex]

The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.

Equation [tex]y = 2x^2 - 6x + 5[/tex]

The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.

Equation [tex]y = x^2 + 7x - 11[/tex]

The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.

Equation [tex]y = -x^2 - 8x - 16[/tex]

The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.

A similar problem is given at https://brainly.com/question/19776811

Solve for c in the equation 3x^2-18x+5=47

Answers

3x²-18x+5=45 is a quadratic equation.
The general quadrilatic equation is ax²+bx+c=0.

So, arranging the equation in this form we get,
3x²-18x+5-47=0
3x²-18x-42=0

The value of C = -42

A-Town wants to know the number of cell phones in each household the town divides the population up by neighborhood and surveys a random number of households and eat what type of survey is this

Answers

It would be a Stratified Survey

Final answer:

A-Town is conducting a survey using a random sample method by dividing the population into neighborhoods and surveying random households in each, which ensures each household has an equal chance of being selected and provides a representative sample.

Explanation:

A-Town's approach to determining the number of cell phones in each household through a survey is an example of a random sample. The method involves dividing the population into neighborhoods and surveying a random selection of households within each area. This technique helps to ensure that every household has an equal chance of being selected, which should provide a representative sample of the town's population. Such methods are necessary to obtain reliable data that reflects the true distribution and characteristics of the target population without regional bias.

Using a representative sample is crucial in research and polling to measure accurately public opinion or collect data on phenomena. As in the given example where the market research firm surveys 500 randomly selected residents to estimate the percentage of adults with cell phones, the firm employs statistical measures like confidence intervals to infer about the entire population's cell phone ownership based on the sample data. Moreover, the concept of probability sampling is also important for achieving a sample that can be generalized to the whole population with reasonable accuracy.

please help with this??

Answers

48, 50, 51, 56, 62, 62, 64, 73, 75
The mode is the number that is repeated more often than any other, so 62 is the mode.

Please help me idk this

Answers

To solve this problem you must apply the proccedure shown below:

1- You have the following information given in the problem above:

- The jug helds 16 cups of milk.
- Isaac drank 1 7/8 cups and his brother drank 1 1/2 cups.

2- Keeping this on mind, you have:

1 7/8=15/8
1 1/2=3/2

=16 cups-15/8 cups-3/2 cups
=101/8 cups

The answer is: 101/8 cups

the mean mark for the class was 70%. There are 30 students in the class, 20 of whom are boys. The mean mark for the boys is 62%. What is the mean mark for the girls?

Answers

Mean mark for the class = 70%
Total marks for the class = 70 x 30 = 2100

Mean mark for the boys = 62%
Total marks for the boys = 62 x 20 = 1240

Total marks for the girls = 2100 - 1240 = 860
Mean marks for the girls = 860 ÷ 10 = 86%

Answer: 86%

A travel website reports that in a particular city, the probability of rain on any day in April is 40%. What is the expected number of rainy days in this city during the month of April?

Answers

There are 30 days in April. To solve this question, we simply multiply the days by the rate:
0.4(30)
(0.4 represents 40%)
Multiply:
0.4(30) = 12
The expected amount of rainy days is 12 days.

What are the coordinates of the vertex of the table? Is it a minimum or a maximum?

x y

0 1

-1 -2

-2 -3

Question 1 options: A.(-4, 1); minimum B.(-2, -3); maximum C.(-2, -3); minimum D.(1, 0); maximum.

pleeeeeeeeez help me

Answers

let
A (0,1)
B(-1,-2)
C(-2,-3)
using a graph tool
see the attached figure

the vertex is the point C (-2,-3) is a minimum

the answer is
minimum (-2, -3)

Which of the following sequences of numbers are arithmetic sequences? Check all that apply.
A.99, 100, 101, 102, 103, ...
B.-3, -5, -7, -9, -11, ...
C.2, -2, 2, -2, 2, ...
D.1, 6, 11, 16, 21, ...
E.-4, 7, -10, 13, -16, ...

Answers

A, B, D
__________________

In an Arithmetic sequence, the difference between two consecutive terms of the sequence remains the same. This difference is known as common difference.

If we observe the given options, we can note:
In option A, the difference between two consecutive terms is the same and is equal to 1.

In option B, the difference between two consecutive terms is the same and is equal to -2.

In option C, the difference is not the same.

In option D, the difference between two consecutive terms is the same and is equal to 5.

In option E, the difference is not the same.

So, the correct options are A,B and D

(2n + 3)(n – 4) = 0
need help asap!!!

Answers

Set each binomial equal to zero to solve.

2n + 3 = 0
2n = - 3
n = - 3 / 2

n - 4 = 0
n = 4

So n = -3/2, 4

In sakura’s garden, for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How many ref flowers are in Sakura’s garden?

Answers

The first thing we must do for this case is to define variables.
We have then:
x: number of red flowers
y: number of yellow flowers.
We write the system of equations:
x + y = 75
y = 2x
Solving the system we have:
x = 25
y = 50
Answer:
there are 25 red flowers in Sakura's garden

The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters

Answers

We assume the question is intended to say there are a total of 20 quarters, nickels, and dimes, the value of which is $2.05. The number of dimes is 3 times the number of quarters.

Let q, n, d represent the numbers of quarters, nickels, and dimes, respectively. Then you have three equations in the unknowns:
q +n +d = 20
25q +5n +10d = 205
-3q +d = 0

A calculator can give the solution to this matrix equation in short order. It is
q = 3
n = 8
d = 9

There are 3 quarters, 8 nickels, and 9 dimes.

_____
If you use the third equation to write an expression for d, you can substitute that into the other two equations.
q +n +3q = 20
25q +5n +10(3q) = 205
Simplifying, these are
4q +n = 20
11q +n = 41
Subtracting the first from the second, we find
7q = 21
q = 3
From there, it is easy to find d=9, n=8.

Help on homework! Which of the following can have a negative effect on your credit score?
A. Getting a promotion at work
B. Late payments on a car loan
C. Paying credit card balances in full
D. low debt-to-income ratio

Answers

Hi there!

The answer is - B.

Hope this helps you!

~DL

Can someone show me how to do this?

16! / 4! 12!

Answers

what do you mean lol, there is no such thing as that in math. if your question is 16/412 then let me know

Jake is younger than Sophie. Sophie is 14 years old. Write an inequality that compares Jake's age in years, (j), to Sophie's age.

Answers

Final answer:

To express that Jake is younger than Sophie who is 14, we use the inequality j < 14, where j symbolizes Jake's age in years.

Explanation:

The question is asking for an inequality that represents Jake's age compared to Sophie's age. Since we are told that Jake is younger than Sophie and Sophie is 14 years old, we can use an inequality symbol to express this relationship. The appropriate inequality is j < 14, where j represents Jake's age in years. The symbol < means 'less than,' which correctly compares Jake's age to Sophie's, indicating that Jake's age is less than 14 years.

Use the graph below to answer the question that follows:

What is the rate of change between the interval x = π and x = three pi over two?
pi over 16
negative 16 over pi
pi over 4
negative 4 over pi

Answers

I just took that test it's -16/pi.

A die is thrown twice. What is the probability that:
1. Neither a doublet ordered pair nor a total of 10 will appear?
2. Neither a multiple of 2 on the first throw nor a total of 6 will appear?
A. 7/9
B. 5/12

Answers

1.) 1/2
2.) B would be your answer.

Answer:

1.)- B. 5/12

2)- A. 7/9

Step-by-step explanation:

Help please??????????

Answers

[tex](13x-13)+(7x-9)=18x+14\\\\13x-13+7x-9=18x+14\\\\20x-22=18x+14\ \ \ |+22\\\\20x=18x+36\ \ \ \ |-18x\\\\2x=36\ \ \ |:2\\\\x=18\\\\|PR|=18x+14[/tex]

substitute the value of x:

[tex]|PR|=18\cdot18+14=324+14=338[/tex]

Convert 7.2*10^-3 to standard form please help thanks

Answers

since it is ^-3, your decimal point is going to go left. or decreasing... 3 movements to be exact. .0072

Your answer would be 0.0072.

=7.2 * 10^−3=7.2 * 1/10*10*10=0.0072

Hope this helps!!

**MARKING BRAINLIEST IF RIGHT AND IF YOU SHOW WORK**
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Show your work.

My teacher said you can use approximate dimensions of the bricks and bathtub. He said use the easiest ones so that it will be easy to solve.

Answers

bath tub: 60 x 30 x 18

brick: 8 x 4 x 2

fermi process:
(60 x 30 x 18) / (8 x 4x 2)

= 32,400 / 64

= 506.25

estimated as 500 bricks

I need Help with this TRIG question

Answers

x
(15) sin 30.5   = ------ (15)
     15

(15) sin 30.5 = x
Plug this part into a calculator.

7.61 = x

Area of a triangle: 1/2bh

1/2 (7.61)(13)
3.805(13)
49.469

49.47 un² is your final answer since you are supposed to round to the tenths place. I hope this helps.

In how many different ways can the letters of the word china be arranged

Answers

There are 5 letters total.

5!= 5*4*3*2*1
5!=120 different options

Someone please help me?

Answers

CBD = 180 - BD/2

CBD = 180 - 98/2

CBD = 180 = 49

CBD = 131

Answer is the third one

Silvia wants to retire at 65 and live on $40,000 a year. How much does she need to save to ensure that her retirement funds last until she is 85?

Select the best answer from the choices provided.
$800,000 because she will need to save for 20 years times $40,000
more than $800,000 because taxes and inflation will increase the value of her savings
less than $800,000 because returns will continue to increase the amount in her savings even after retirement
more than $800,000 because compound return will reduce her savings

Answers

She must save 800,000 because that's how much she'll need in those 20 years of retirement. The first choice is correct.

Answer:

$800,000 because she will need to save for 20 years times $40,000

Step-by-step explanation:

Silvia wants to retire at 65 and live on $40,000 a year.

She wants to live till 85 and retire at 65 years.

So, number of years to save = [tex]85 -65= 20[/tex]

And she needs to save [tex]40000\times20=800000[/tex]

Hence, she must save 800,000.

Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what is the probability that he will randomly select a blue marble, without replacement, and then a purple marble from the jar

Answers

To find the probability of both of these occurring, you will multiply the probability of choosing a blue marble by the probability of choosing a purple marble (with no replacement after the first one).

Probability of choosing a blue marble: 17/120
Probability of choosing a purple marble: 18/119

17/120 x 18/119 = 3/140

You will have a 3/140 chance of both of these occurring.

The probability of selecting a blue marble followed by a purple marble from a jar containing 120 marbles with different colors is approximately 2.2%.

The probability of grabbing a blue marble and then a purple marble is determined by multiplying the probability of grabbing a blue marble first and the probability of grabbing a purple marble second. Here's the calculation:

Probability of selecting a blue marble first: 17/120

Probability of selecting a purple marble second (after one blue marble is already taken out): 18/119

Multiplying the probabilities: (17/120) * (18/119) ≈ 0.022, or 2.2%

Please help me idk this

Answers

Answer:

1 13/20

Step-by-step explanation:

You want the total of distances walked to be the length of the hike:

2 1/10 + 1 1/4 + (left to walk) = 5

Then the amount left to walk is the difference ...

left to walk = 5 - 2 1/10 - 1 1/4

___

You are expected to know how to do arithmetic with mixed numbers, and/or to be able to use a calculator for the purpose.

5 - 2 1/10 - 1 1/4

= (5 -2 -1/10) - 1 1/4

= 2 9/10 - 1 1/4

= (2 -1) + (9/10 -1/4)

= 1 + (9/10 -1/4)

= 1 + (18/20 - 5/20)

= 1 13/20 . . . miles left to walk

___

Using a calculator:

5 -2.1 -1.25 = 1.65 = 1 65/100 = 1 13/20

Your job pays 6$ per hour write a variable expression for your pay in dollars for working h hours what is your Pay if you work 32 hours

Answers

6h

Fill in 32 for h

6x32

For 32 hours, you would earn $192

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